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Journal of Marine Science and Technology

, Volume 13, Issue 3, pp 190–206 | Cite as

Sail optimization for upwind sailing: application in a Tornado, the Olympic class catamaran

  • Ana Laverón-Simavilla
  • Victoria Lapuerta
  • Sebastián Franchini
  • Angel Sanz
Original Article

Abstract

A study of a boat's motion is carried out in order to analyze the aerodynamic properties of the optimal sail for obtaining the maximum velocity when sailing to windward. The mechanics study shows the optimal C L and C D for a given sail and how the shape of the aerodynamic polar of the sail should be. A parametrical analysis of the aerodynamics of a sail is then carried out varying the maximum camber, position of the maximum camber in the chord direction and position of the maximum camber in the mast direction. The parametric analysis is done numerically with a vortex lattice method (VLM) and experimentally in a wind tunnel. The results show that the influence of the relevant parameters studied can be reduced to the variation of two parameters, A and B, defining the polar of the sail, C DA 2 C L 2; and the influence of parameters A and B on the maximum VMG obtainable are calculated.

Keywords

Sailboats Optimization Aerodynamics 

List of symbols

A

coefficient of the polar of the sail defined as \( C_{{\text{D}}} = B + A^{2} C_{{\text{L}}}^{2} \)

b

sail span

B

coefficient of the polar of the sail defined as \( C_{{\text{D}}} = B + A^{2} C_{{\text{L}}}^{2} \)

C

profile chord

CD

drag coefficient

CHx

hydrodynamic force coefficient in the direction normal to the yacht speed

CHy

hydrodynamic force coefficient in the direction of the yacht speed

CL

lift coefficient

CLopt

optimal sailing lift coefficient

CM

heeling moment coefficient made dimensionless with the apparent wind velocity

\( C_{{\text{M}}}^{*} \)

heeling moment coefficient made dimensionless with the true wind velocity

Cr

chord of the root section of the sail

Ct

chord of the tip section of the sail

D

drag

\( \vec F_{\rm A} \)

aerodynamic force

\( \vec F_{{\text{\rm H}}} \)

hydrodynamic force

Fn

Froud number, \( F_{n} = \frac{{\left| {\vec V_{s} } \right|}}{{\sqrt {gD_{{\text{h}}} } }} ,\) where g is the gravity and D h is the characteristic length scale of hydraulic depth

K

\( \frac{{\rho _{{{\text{H}}_{ 2} {\text{O}}}} S_{{\text{H}}} }}{{\rho _{{\text{a}}} S_{{\text{A}}} }} \)

L

lift

m

maximum camber of the profile expressed as a percentage of its chord length

mτ

slope of the twist profile

RnA

aerodynamic Reynolds number, \( R_{{n{\text{A}}}} = \rho _{a} \frac{{\left| {V_{{\text{A}}} } \right|\bar C_{{\text{A}}} }}{{\mu _{{\text{A}}} }} \), being \( \bar C_{{\text{A}}} \) the media chord of the sail and μ A the dynamic viscosity of the water

RnH

hydrodynamic Reynolds number, \( R_{{{\it{n}\text{H}}}} = \rho _{{{\text{H}}_{ 2} {\text{O}}}} \frac{{V_{{\text{s}}} L_{{{\text{hull}}}} }}{{\mu _{{{\text{H}}_{ 2} {\text{O}}}} }}, \) being L hull the length of the hull and \( \mu _{{{\text{H}}_{ 2} {\text{O}}}} \) the dynamic viscosity of the air

SA

characteristic area of the sail

SH

characteristic area of the hull

\( \overrightarrow {V_{{\text{A}}} } \)

apparent wind speed

VMG

Velocity Made Good

Vmg

velocity made good

\( \overrightarrow {V_{{\text{S}}} } \)

yacht speed

\( \overrightarrow {V_{{\text{T}}} } \)

wind speed

ρa

air density

\( \rho _{{{\text{H}}_{ 2} {\text{O}}}} \)

water density

α

angle of attack of the sail

λ

drift angle

ηA

aerodynamic efficiency of the sail

ηH

hydrodynamic efficiency of the hull

ηm

location of the profile with maximum camber along the mast direction as a percentage of the sail span

ξm

location of the maximum camber along the chord of the profile expressed as a percentage of the chord

μ

taper ratio

τ

twist angle of each profile

Notes

Acknowledgments

This work has been sponsored by the Spanish Consejo Superior de Deportes (CSD) and by the Universidad Politécnica de Madrid (UPM) and is part of a more general endeavour for the study of sails design.

References

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Copyright information

© JASNAOE 2008

Authors and Affiliations

  • Ana Laverón-Simavilla
    • 1
  • Victoria Lapuerta
    • 1
  • Sebastián Franchini
    • 1
  • Angel Sanz
    • 1
  1. 1.E.T.S.I. AeronáuticosUniversidad Politécnica de MadridMadridSpain

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